Various investigations were undertaken to establish the foundations of optically-based biomedical measurement techniques. Thus, we worked on mathematical models to link the fundamental optical properties of biological tissue to measureable quantities such as the diffuse surface reflectance or time- resolved transmittance, needed to develop noninvasive therapeutic and diagnostic applications of light in medicine. Particular attention was given to understanding how light is transmitted within materials when optical heterogeneity is important, for example in media which contain statistically disordered internal boundaries (e.g., lung, bone tissue microvasculature). We showed how the intensities and pathlengths of photons reemitted at an illuminated surface depend on the fractal dimensions of scattering inclusions and other internal structures. We also examined whether light might be used to detect small absorptive inclusions hidden in a multiply-scattering optical medium. Such studies were undertaken to support development of technologies which have as their goal the noninvasive detection of tumors or other optically distinguishable targets. Numerical methods were devised to facilitate computer analysis of schemes that utilize diffusely reflected or transmitted light to locate a hidden object. Computer simulations also were performed to understand how the probabilistic nature of photon migration affects laboratory measurements of reemitted light intensities. We also were involved in several projects that use scattering and other measurement techniques to examine relationships between the physical properties and molecular structure of biological and chemical gels. Several of the latter are important in various areas of biotechnology, and protein gels and other extended polymer matrices play significant roles in many cell biological processes (e.g., cell cotility and wound healing). In collaboration with other researchers, we used rheological techniques to characterize the intermolecular bonds of proteoglycan cellular matrix material. We also performed small-angle neutron scattering (SANS) measurements to examine interactions occuring between polymer strands in agarose gels. These studies were undertaken to extend our general knowledge of the behaviors of this important class of biological materials, as well as to characterize the particular samples chosen for study.